Aubameyang opened Arsenal's scoring with a goal just five minutes in, while Ainsley Maitland-Niles made it 2-0 with a score of his own of an Aubameyang assist in the 15th minute.
That goal proved pivotal as Arsenal went through to the last eight.
Rennes gave Arsenal a real scare shortly after the half-time restart as Ismaila Sarr picked out the post with his shot, which took a touch on its way through, after Shkodran Mustafi was caught on the ball.
Arsenal have overcome Manchester United and Rennes in quick succession, and the striker has been a key man in both matches.
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Unai Emery will not care though and he said after the game that he is "proud" of his players.
"This comeback was very hard, but I think the reaction was very good from every player", Emery told reporters.
"Playing under pressure is good, growing up under pressure - with each player playing like a team and feeling the hard moments to give us our best performance", Emery said.
Aubameyang missed two big chances inside a minute to complete his first hat-trick in Arsenal colours, poking wide of the post with just Koubek to beat and then skewing wide of the same post once teed up by Ramsey in front of goal. "And the last teams, they are all very important, and it's going to be very hard", Emery said.
"For us, today and Sunday, we are aware of playing competitively and I think it is good confidence for us to feel that".